structural steelwork
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Structural Eurocodes
W.M.C. McKenzie B.Sc., Ph.D., C.Phys., M.Inst.P., C.Eng.SOEBE, Edinburgh Napier University
The Design of Structural Steelwork
to EN 1993 (EC3)
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This evenings presentation
1. Introduction to, and development of, the Eurocodes
2. Design of structural steelwork to EN 1993-1 (EC3)
3. Sources of information
Dr. W.M.C. McKenzie2
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The Construction Products Directive (CPD) Council
Directive 89/106/EEC, is one of over 20 New Approach
Directives whose aim is to breakdown artificial barriers
to trade throughout the EU and is intended for products
placed on the market.
(EEC initiated the programme in 1975.)
The Construction Products Directive
Dr. W.M.C. McKenzie3
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Essential Requirements to be satisfied byproducts suitable for construction:
Dr. W.M.C. McKenzie4
1. Mechanical resistance and stability.
2. Safety in case of fire.
3. Hygiene, health and the environment.
4. Safety in use.
5. Protection against noise.
6. Energy, economy and heat retention.
Applicable to the Eurocodes.
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CE marking is mandatory for products covered by a Directive
and allows them to circulate freely within the European
Economic Area.
It follows the successful approval of a product and symbolises
the conformity of the product with the Directive.
The use of Eurocodes raises a presumption of conformity with
Essential Requirement 1, and parts of Essential Requirements 2
and 4 of the Construction Products Directive.
CE Marking:
Dr. W.M.C. McKenzie5
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A set of European Standards (e.g. EN 1993-1-1) for the design of
buildings and other civil engineering works and construction
products, produced by the Comit Europen de Normalisation
(CEN)the European Committee for Standardisation.
(The programme to establish ENs began in 1989).
They embody National experience and research output, together
with the expertise of CEN Technical Committee 250
(CEN/TC250)and other international technical organisations.
What are Eurocodes?
Dr. W.M.C. McKenzie6
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The Eurocode Suite
Dr. W.M.C. McKenzie7
EN 1990 Eurocode Basis of Structural Design
EN 1991 Eurocode 1 Actions on Structures
EN 1992 Eurocode 2 Design of Concrete Structures
EN 1993 Eurocode 3 Design of Steel Structures
EN 1994 Eurocode 4 Design of Composite Steel & Concrete Structures
EN 1995 Eurocode 5 Design of Timber Structures
EN 1996 Eurocode 6 Design of Masonry Structures
EN 1997 Eurocode 7 Geotechnical Design
EN 1998 Eurocode 8 Design of Structures for Earthquake Resistance
EN 1999 Eurocode 9 Design of Aluminium Structures
(Note:an additional code is currently being developed for the use
of structural glass.)
Table 1
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EN 1991 Parts 1 to 4:
Eurocode 1
Part 2: Traffic Load
Part 1-1: Densities/self-
weights & Imposed loads
Part 1-3: Snow
Part 1-2: Fire
Part 1-5: Thermal Actions
Part 1-6: Actions during
execution
Part 1-7: Accidental Actions
Part 1-4: Wind Actions
Part 3: Cranes & Machinery
Part 4: Silos & Tanks
National Annexes
Figure 1
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The Links Between the Eurocodes
Dr. W.M.C. McKenzie9
EN 1990
Head Eurocode
Structural safety, serviceability,durability and robustness
EN 1991 Actions on structures
EN 1998EN 1997 Geotechnical and seismic design
Design and detailing
EN 1992 EN 1993 EN 1994
EN 1995 EN 1996 EN 1999
Figure 2
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Why Use the Eurocodes?
Dr. W.M.C. McKenzie10
They comprise a complete set of design standardsthat cover
all principal construction materials and all major fields of
structural engineering.
They are the most advanced codes of practice in the world.
they are flexible, offering the possibility for each country to
choose levels of safety through Nationally Determined
Parameters (NDPs).
They provide design methods whose development has been
fully transparent, and promote innovation in structural
design.
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Benefits and Opportunities
Dr. W.M.C. McKenzie11
They lead to more uniform levels of safety in construction
throughout Europe.
They provide common design criteria and methodsto fulfil
the specified requirements for mechanical resistance, stability
and resistance to fire, including aspects of durability and
economy.
They provide a common understanding between owners,
operators and users, designers, contractors and manufacturers.
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Benefits and Opportunities (cont.)
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They provide a common and transparent basis for fair
competition in the construction market.
They facilitate the exchangeof construction services.
They allow the preparation of common design
aids/software and a common basis for research and
development.
They increase the competitiveness of the European civil
engineering firms, contractors, designers and product
manufacturers in their world-wide activities.
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Examples of Structures Designed Using the Draft(ENV) and Final (EN) versions of Eurocodes
Roof of the Lige railway station, Belgium(ENV 1991- loading & ENV 1993 - steelwork)
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Bridge over Wadi Dib, Algeria(EN 1998earthquake design)
Roccaprebalza Viaduct, Italy
(EN 1992, EN 1993 & EN 1994) S. Gabriel and S. Rafael Towers, Portugal
(EN 1994, - composite construction)Figure 3
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CEN committee structure
e.g. The sub-committee for Eurocode 3 for
the design of steel structures:CEN/TC 250/SC 3
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CEN
SC 0 SC 1 SC 2 SC ....SC 3
TC 250 TC ...... TC ......TC ......
Figure 4
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The implementation of an EN Eurocode Part by National
Authorities and National Standards Bodies after is made
available by CEN [i.e. Date of Availability (DAV)] has
three phases:
1. Translation period,
2. National Calibration period,
3. Coexistence period.
15
National Implementation of Eurocode Part
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National Calibration Period: maximum 2 years
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1. The Member States fix the Nationally Determined Parameters
(NDPs).
2. At the end of the period, the national version of the Eurocode Part
with the National Annex, should be published by the National
Standards Body.
3. The Member States should adapt the National Provisions so that
the Eurocode Part can be used on their territory.
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Coexistence Period: maximum 3 years
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1. During this period the Eurocode Parts can be used in parallel with
the existing code system.
2. The coexistence period of a Eurocode Packagewill last up to a
maximum time of three years after the national publication of the
last Part of a Package.
3. Member States should ensure that all the Parts of a related Package
can be used without ambiguity.
4. At the end of the coexistence period all conflicting National
Standards should be withdrawn.
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Parts
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All of the EN Eurocodes relating to materials have a Part 1-1 which
covers the design of buildings and other civil engineering structures and a
Part 1-2for fire design. The codes for concrete, steel, composite steel and
concrete, and timber structures and earthquake resistance have a Part 2
covering design of bridges. These Parts 2 should be used in combination
with the appropriate general Parts (Parts 1).
Part 1-1
General
rules andrules for
buildings
Part 1-2
Structural
Fire Design
Part 2
Bridges
Part 3...
.............
Figure 5
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The EN Eurocode Parts have been grouped into Packages, each
of which must be published before the implementation of that set
of EN Eurocodes may begin. EN 1990, EN 1991, EN 1997 and
EN 1998 are material independent and are therefore included in
each package.
Packages
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Packages (cont.)
A Package is a group of EN Eurocode Parts that are needed for a
particular design (e.g. for a building, a bridge, a silo, a tank or a
pipeline).
The purpose of defining packages, by grouping Parts of EN
Eurocodes, is to enable a common Date of Withdrawal (DoW)
for all of the relevant National Standards that are needed for a
particular design.
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Packages (cont.)
When a National standard has a wider scope than the conflicting
EN Eurocode Package, only that part of the National standard
whose scope is covered by the Package has to be withdrawn.
When more than one package of EN Eurocodes is likely to be
needed for the design of works, the dates of withdrawal of the
related Packages can be synchronized.
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3/1: Design of steel building and civil engineering structures
(excluding bridges, silos, tanks and pipelines, steel piling,
crane supporting structures, and towers and masts).
3/2: Design of steel bridges.
3/3: Design of steel silos, tanks and pipelines.
3/4: Design of steel piling.
3/5: Design of steel crane-supporting structure
Eurocode 3 Packages: Steel Structures
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Package 2.1Concrete Building and Civil Engineering Structures
Courtesy H. GulvanessianFigure 6
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Eurocodes Timeline:Duties of National Authorities & Standards Bodies
25
National Implementation of Eurocode Part
Maximum 2 years Maximum 3 years
Date of Availability
(DAV)
Publication of Part and
National Annex
Fixing Nationally
Determined
Parameters (NDPs)
Adaptation of NationalProvisions to allow use
of Eurocodes
Translation toNational Language
Final Adaptation ofNational Provisions
Withdrawal of all conflicting
National Standards by March 2010
Note: Publication of the Eurocodes
was completed in May 2007
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Maximum period of 5 years
Figure 7
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54 complete4 awaited
26
UK - Eurocode Parts and Annexes Published
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58 Parts in total
Figure 8
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Are the EN Eurocodes Mandatory?
Dr. W.M.C. McKenzie27
Under the Public Procurement Directive,
it is mandatory that Member States accept designs to the
EN Eurocodes. The EN Eurocodes will become the standard
technical specification for all public works contracts. If
proposing an alternative design one must demonstrate that
istechnical ly equivalentto an EN Eurocode solution.
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Are the EN Eurocodes Mandatory? (cont.)
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Technical equivalence
A contracting authority "cannot reject a tender on the
grounds that the products and services tendered for do not
comply with the specifications to which it has referred,
once the tenderer proves in his tender to the satisfaction of
the contracting authority, by whatever appropriate means,
that the solutions which he proposes satisfy in an
equivalent manner the requirements defined by the
technical specifications."
Directive 2004/18/EC of the European Parliament and of the Council of 31 March 2004.
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Are the EN Eurocodes Mandatory? (cont.)
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Technical equivalence may be admissible provided it
is shown that the alternative rules accord with the
relevant Principles of the EN Eurocodes and are at
least equivalentwith regard to mechanical resistance,
stability, fire resistance and durability which would be
expected using the EN Eurocodes.
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Are the EN Eurocodes Mandatory? (cont.)
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As the National Standardisation Bodies are not expected to
maintain the withdrawn National Standards in practice,
there will be little option but to use the EN Eurocodes. It is
extremely likely that pressures from international clients
and contractors, as well as other stakeholders like the
insurance industry, will lead to their more rapid application
for private construction.
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Are the EN Eurocodes Mandatory? (cont.)
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For the purpose of products obtaining CE
marking under the Construction Products Directive,
Member States should refer to the EN Eurocodes in
their national provisions on structural construction
products, thus making them mandatory for this
purpose.
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National Title Page National Foreword EN Title Page
EN Text EN Annexes National AnnexFigure 9
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EN Annexes are either:
1. Normative containing information which must be
followed.
or
2. Informative containing supplementary information
which maybe followed.
EN Annexes
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EN Annexes: e g in EN 1993-1-1 & EN 1993-1-5
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EN Annexes: e.g. in EN 1993-1-1 & EN 1993-1-5structural steelwork
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Figure 10
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National Annexes
A National Annex (NA) is the linkbetween a Eurocode and
the National Standards for a Member State.
It contains rules and parameters to ensure safety remains a
National, and not a European, responsibility.
The foreword of each Eurocode Part lists paragraphs in which
national choice is allowed. However, the National Annex has
limited overriding authority to the Eurocode.
Dr. W.M.C. McKenzie35
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National Annexes (cont.)
ANational Annex cannot change or modify the
content of the EN Eurocode text in any way other than
where it indicates that national choices may be made by
means of Nationally Determined Parameters.
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Guidance Paper L(see http://eurocodes.jrc.ec.europa.eu )
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National Annexes (cont.)
The National Annex reflects specific needs of individual countries in
the Eurocode.
A National Annex exists for each Eurocode Part.
National Annexes provide:
Nationally Determined Parameters (NDPs),
Country specific data (e.g. snow maps, wind maps etc.),
Procedures to be used where a choice is offered,
Guidance on the informative annexes,
Reference to non-contradictory, complementary information,
(NCCI)
Dr. W.M.C. McKenzie37
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Nationally Determined Parameters
EN Eurocodes recognise the responsibility of regulatory
authorities in each Member State and have safeguarded their
right to determine values related to regulatory safety matters
at a national level where these continue to vary from State to
State.
EN Eurocodes provide for National Choices, full sets of
recommended values, classes, symbols and alternative
methods to be used as Nationally Determined Parameters
(NDPs).
Dr. W.M.C. McKenzie38
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Nationally Determined Parameters (cont.)
When the EN Eurocodes are used for the design of
construction works, or parts thereof, the NDPs of the
Member State on whose territory the works are located shall
be applied, e.g.
Dr. W.M.C. McKenzie39
Characteristic snow load on the ground:
sk
EN 1991-1-3:Annex C
Ground snow load map
UK National AnnexGround snow load map
Figure 11
i i ( )
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Nationally Determined Parameters (cont.)Extract from
UK National Annex to EN 1993-1-1:
Design of steel structures
Part 1-1: General rules and rules for
buildings
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Note:
A National Standardisation Board is not
permitted to publish a National version of a
Eurocode with the NDPs from the National
Annex incorporated in to the EN text.
(Users may find it useful to mark up their
own copies of the EN from the NA.)
Figure 12
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Nationally Determined Parameters (cont.)
Database of Nationally Determined Parameters
A database with the Nationally Determined Parameters adopted
in the EU and The European Free Trade Association (EFTA)
countries implementing the EN Eurocodes will constitute the
basis for the analysis of the NDPs and for the definition of
strategies tending to achieve further convergence and
consequently aiming at facilitating the achievement of the
European Single Market for construction works and structural
construction products.
Dr. W.M.C. McKenzie41
Nationally Determined Parameters (cont )
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Nationally Determined Parameters (cont.)
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Extract from the database of Nationally Determined Parameters
Progress of uploading of
NDPs (October 2009)
Uploaded
NDPs
Not registered
Registered
25%53%
22%
Figure 13
Last updated: 4th. September 2009
Source: http://eurocodes.jrc.ec.europa.eu
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Non-contradictory Complimentary Information
Most existing national codes include some provisions that
are not in the Eurocodes. Provided that the material is
consistent with the Eurocodes, it can be advisory or a
requirement in that country. It is known as "non
contradictory complimentary information(NCCI).
Dr. W.M.C. McKenzie43
Non contradictory Complimentary Information (cont )
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Non-contradictory Complimentary Information (cont.)
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Figure 14
Non contradictory Complimentary Information (cont )
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Non-contradictory Complimentary Information (cont.)
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Figure 15
Principles and Application R les
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Principles and Application Rules
The Clauses given in the Eurocodes are either:
Principles or Application Rules
The Principles are general statements, definitions,
requirements or analytical models for which there is no
alternative permitted. They are identified by (P) after the
clause number.
The Application Rulesare generally recognised rules whichare recommended methodsof achieving the Principles.
Dr. W.M.C. McKenzie46
Ultimate Limit States (cont)
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Ultimate Limit States (cont)
The Ultimate Limit States are considered in four categories in
the Eurocode. They are:
(i) EQU: relating to the static equilibrium of a structure or
any part of it which is considered as a rigid body,
(ii) STR: relating to internal failure or excessive deformation
of a structure or structural member,
(iii) GEO: relating to failure or excessive deformation of the
ground,
(iv) FAT: relating to fatigue failure of structural members.
Dr. W.M.C. McKenzie47
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Differences From British Standards
BSs have no equivalent to Eurocode EN1990:
(establishes for all structural Eurocodes, the Principles and
Requirements for safety, serviceability and durability.
Traditionally in BSs this has been replicated in each code
separately.)
The structure of the Eurocodes is phenomenon basedrather
than member basedas in the British Standards.
Dr. W.M.C. McKenzie48
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Differences From British Standards (cont.)
EN 1991 uses different load combinations from the BSs:
Three different types of combination are given in the Eurocode.
They are:
combinations of actions for persistent or transient design
situations (fundamental combinations),
combinations of actions for accidental design situations,
combinations of actions for seismic design situations.
Dr. W.M.C. McKenzie49
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Differences From British Standards (cont.)
The Eurocodes do not provide standard /derived formulae
these are considered to be textbook material; e.g. in steel
design, the formula to determine the elastic critical moment
(Mcr) required to evaluate the lateral torsional bucklingresistance is not given, (see NCCIs from the access steel
website or other sources).
The unit of stress is the MPa (in UK refer to N/mm2)
although not consistently so.
Dr. W.M.C. McKenzie50
Diff F B iti h St d d ( t )
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Differences From British Standards (cont.)
The axes are different from that traditionally used in the UK:
Dr. W.M.C. McKenzie51
z
z
x
x
y
y
y
z
z
x
x
y
Eurocode System UK System
There are implications when considering instability andslenderness calculations!
Figure 16
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Differences From British Standards (cont.)
Beware of inconsistent symbol definitions, e.g. EN 1993:1-1
Dr. W.M.C. McKenzie53
Figure 17
Differences From British Standards (cont )
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Standard ISO practice has been adopted in representing
a decimal point by a comma, i.e. 5,3 5.3. In the UK, to
avoid confusion, engineers should avoid using a comma
to indicate thousands (as is common practice) if they do
not adopt Standard ISO practice, i.e.
3534.1 3.5341 1033534,1 3,5341 103 (Not 3,534.1)
Dr. W.M.C. McKenzie54
Differences From British Standards (cont.)
T i l
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Terminology
Actions:
Permanent/variable loads, imposed displacements, thermalstrains etc.
Effects:
Internal axial forces, shear forces, bending moments etc.
Resistance:Capacity of structural elements to resist design effects.
Verification:
Checking the suitability of structural sections.
Execution:
Fabrication, erection etc. of construction.
Symbols
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Symbols
Design value of an effect: subscript (Ed)
e.g. MEd design bending moment.
Design value of the resistance: subscript (Rd)
e.g. MRd design resistance for bending moment.
Elastic section property: subscript (el)
e.g. Wel elastic section modulus.
Plastic section property: subscript (pl)
e.g. Wpl plastic section modulus.
Effective section property: subscript (eff)
e.g. Aeff elastic section modulus.
Acronyms
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Acronyms
CEN Comit Europen de Normalisation.
CPD Construction Products Directive.
NA National Annex.
NDP Nationally Determined Parameter.
NCCI Non-contradictory Complimentary Information.
DAV Day of Availability.
ENV Draft Version of a Code Part for comment. (DD ENV)
EN EuroNorm: Final Version of a Code.
DoW Date of Withdrawal.
Dr. W.M.C. McKenzie57
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Design Situationsand
Load Combinations to EN 1990
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Design Situations (EN 1990)
Persistent:e.g. normal use of a structure.
Transient:
e.g. temporary situations, e.g. execution.
Accidental:
e.g. exceptional events, e.g. fire, impact explosion.
Seismic:e.g. effects of earthquake loading .
Ultimate Limit State Combinations (EN 1990)
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Ultimate Limit State Combinations (EN 1990)
For persistent and transient design situations:
G,j k,j Q,1 k,1 Q,j 0,i k,i1 1 Equation (6.10)
pj iG P Q Q
G,j k,j Q,1 0,1 k,1 Q,j 0,i k,i
1 1
Equation (6.10a)pj i
G P Q Q
For Equilibrium limit states (EQU) only Equation (6.10) should be used. For
Strength limit states (STR) and Geotechnic limit states (GEO) either
Equation (6.10) or the less favourable of (Equation (6.10a) and (6.10b) may
be used.
j G,j k,j Q,1 k,1 Q,j 0,i k,i
1 1
Equation (6.10b)pj i
G P Q Q
leading variable accompanying variables
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Ultimate Limit State Combinations (EN 1990)
For accidental design situations:
where1,1
Qk,1
or2,1
Qk,1
is dependent on the accidental situation e.g.
impact, fire etc.
For seismic design situations:
k,j 1,1 2,1 k,1 0,i k,i1 1
or Equation (6.11b)dj i
G P A Q Q
k,j 0,i k,i
1 1
Equation (6.12b)Edj i
G P A Q
Serviceability Limit State Combinations (EN 1990)
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Serviceability Limit State Combinations (EN 1990)
Characteristic combinations:
This should be used when considering an irreversible serviceability
limit state, functioning of a structure, damage to finishes or non-
structural elements e.g. partition walls, caused by excessive deflection.
Frequent combinations:
This should be used when considering reversible limit states, e.g. non-permanent displacement of a floor supporting a machine that is
sensitive to vertical alignment, avoiding ponding of water etc.
Quasi-permanent combinations:
This should be used when considering reversible limit states or long-
term effects, e.g. when considering appearance, creep etc.
Serviceability Limit State Combinations (EN 1990)
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Serviceability Limit State Combinations (EN 1990)
For characteristic combinations:
For frequent combinations:
For quasi-permanent combinations:
k,j k,1 0,i k,i1 1
Equation (6.14b)pj i
G P Q Q
k,j 1,1 k,1 2,i k,i
1 1 Equation (6.15b)p
j iG P Q Q
k,j 2,i k,i
1 1
Equation (6.16b)j i
G P Q
UK N.A. to EN 1993 indicates that only variable loads should be considered.
Design of structural steelwork to EN 1993
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Design of structural steelwork to EN 1993
BS 4491 Part: 120 A5 pages / 77 A4 pages
(1969metric version, original version 1932)
BS 59509 Parts: 569 A4 pages
(1990)
EN 199320 Parts: 1291 A4 pages
(March 2010conflicting codes withdrawn)
Design of Structural Steelwork to EN 1993-1
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Design of Structural Steelwork to EN 1993 1
EN 1993-1 comprises twelve parts. In most cases the following
parts will be required:
EN 1993-1-1:General rules and rules for buildings.
EN 1993-1-2:Structural fire design.
EN 1993-1-3:Cold formed thin gauge members and sheeting.
EN 1993-1-5:Plated structural elements.
EN 1993-1-8:Design of joints.
EN 1993-1-10: Selection of steel for fracture toughness and
through-thickness properties.
Material Properties: yield strength (fy) and ultimate
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Material Properties: yield strength (fy) and ultimatestrength (fu)
Values for the yield strength and the ultimate strength of steel are given in
Table 3.1 of EN1993-1-1:2005 (E) for a range of steel grades and
thicknesses.
Figure 18
non-alloy
structural steels
?
Material Properties: yield strength (fy) and ultimate
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Material Properties: yield strength (fy) and ultimatestrength (fu)
The UK NA indicates that the values of yield strength fyand the ultimate
strengthfushould be obtained from the product standard e.g. EN 10025-2.
Figure 19
= fy = fu
Material Properties: comparison of EN 1993-1-1 and
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p p N 3EN 10025-2
A comparison of the EN1993-1-1 and the EN10025-2 values is given in
Table 2 below.
Table 2
Steel grade
EN 1993-1-1 EN 10025-2
Thickness
(mm) fy (MPa)
Thickness
(mm) fy (MPa)
S275 t 40 275 t 16 275
16
-
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ate a ope t es: ou g s odu us, s ea odu us,Poissons ratio and the coefficient of thermal expansion
Values of the standard elastic material coefficients is given in Clause 3.2.6
as follows:
Modulus of elasticityE= 210 103 MPa
Shear Modulus G 81 103 MPa
PoissonsRatio = 0,3
Coefficient of thermal expansion= 12 10-6/K (forT100C)
(Note:for composite concrete-steel construction = 1010-6/K)
Partial Factors for Material Strength (Mi)
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g ( Mi)
The material partial safety factors are dependent on the resistance being
checked as follows:
M0 is used when verifying the resistance of cross-sections of any class,M1 is used when verifying the resistance of members to instability assessed
by member checks,
M2 is used when verifying the resistance of tension members to fracture.The values given in the UK N.A. are:
M0 = 1,0; M1 = 1,0; M2 = 1,1Values to be used for the resistance of joints are given in EN1993-1-8:
M0toM7depending on the element being considered, i.e. bolt, weld, pin etc.
Conventions for Member Axes
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Figure 20
z-z
y-y
x-x
Ultimate Limit States: Elastic Verification for Resistance
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Verification may be carried out using the von Mises yield criterion where
the interaction of local stresses are limited to thefy/M0as follows:
where:
x,Edis the design value of the local longitudinal stress,
z,Edis the design value of the local transverse stress,
Ed is the design value of the local shear stress.
This can be conservative and does not include any partial plastic stress
distribution and should only be used when interaction on the basis of
resistancesNRd,MRdandVRdcannot be carried out.
2 2 2
x,Ed z,Ed x,Ed z,Ed Ed
y M0 y M0 y M0 y M0 y M0
3 1,0f f f f f
Ultimate Limit States: Verification for Section Resistance
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Verification is carried out where appropriate for sections at the ultimate
limit state in relation to member forces and moments: tension resistance, (NEd /Nt,Rd 1,0) Clause 6.2.3 compression resistance, (NEd /Nc,Rd 1,0)Clause 6.2.4 bending resistance, (MEd /Mc,Rd 1,0)Clause 6.2.5 shear resistance, (VEd /Vv,Rd 1,0)Clause 6.2.6 torsional moment resistance, (TEd /TRd 1,0)Clause 6.2.7 combined bending and shear resistance Clause 6.2.8
combined bending and axial resistance Clause 6.2.9 and
combined bending, shear and axial resistanceClause 6.2.10.
Tension Resistance
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Nt,Rdis taken as the smaller of:
(a) yielding of the gross-cross-section to prevent
excessive deformation of the member.
or
(b) ultimate resistance of the net cross-section at
holes for fasteners.
The 0,9 enabled the harmonization of the Mfactor with that used for the
resistance of other connecting parts, i.e. bolts, welds etc. (M0toM7)
Anet is the gross-area less appropriate deductions for all holes and other
openings.
y
pl,RdM0
Af
N
net uu,Rd
M2
0,9A f
N
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Bending Resistance
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Mc,Rdis taken as follows:
(a) for Class 1 or Class 2.
(b) for Class 3 cross-sections.
(c) for Class 4 cross-sections.
Fastener holes in the tension flange may be ignored provided that for the tension
flange: (see Clauses 6.2.5(4)/(5)).
Except for oversize and slotted holes and provided that they are filled with
fasteners, no allowance need be made in the compression zone for holes,.
pl y
c,Rd p,Rd
M0
W fM M
el,min y
c,Rd el,Rd
M0
W fM M
eff,min y
c,Rd el,RdM0
W fM M
f yf,net u
M2 M0
0,9 A fA f
Shear Resistance
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Vc,Rdis taken as follows:
whereAvis the shear area, e.g. for rolled Iand Hsections:
Av= A2btf+ (tw+ 2r)tf hwtw
is a shear area factor to allow for an increase due to strain hardening.
A value of = 1,2 is given in EN 1993-1-5 for steel grades up to and
including S 460.
In the UK National Annex a value of =1,0 is to be taken for all gradesof steel.
Shear buckling need not be checked for unstiffened webs if
v y
c,Rd p,Rd
M0 3
A fV V
w
w
72h
t
Torsional Moment Resistance
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TRdis taken as follows:
whereTt,Ed andTw,Edare the St.Venant torsion and the warping torsion
respectively.
As a simplification for closed hollow cross-sections (i.e. those with high
torsional rigidities) torsional warping can be neglected. For open sections
e.g. IofHsections (i.e. those with low torsional rigidities), the St. Venanttorsion may be neglected.
Torsion combined with bending, shear and axial forces are also covered.
Rd
Ed t,Ed w,Ed
is the torsional resistance of the cross-sectionTT T T
Combined Shear Force and Torsional Moment Resistance
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The design shear force should satisfy the following expressions using a
reduced plastic shear resistance: where:
forIand Hsections:
for a channel section:
for a structural hollow section:
Ed
pl,T,Rd
1,0V
V
t,Edpl,T,Rd pl,Rdy M01 1,25 3V Vf
t,Ed w,Ed
pl,T,Rd pl,Rd
y M0 y M0
11, 25 3 3
V Vf f
t,Edpl,T,Rd pl,Rdy M01 3V Vf
Combined Bending and Shear Resistance
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g
In most cases the effect of the shear force on the moment of
resistance can be neglected i.e. whenVEd
< 0,5Vc,Rd
In cases where this is not satisfied there are two options:
1 Use a reduced yield strength for the shear area to determine the
reduced moment of resistance, i.e.fy,reduced = (1 )fywhere
2 For I-sections with equal flanges and bending about the major
axis: and Aw=hwtw
2
Ed
pl,Rd
21
V
V
2w
pl,y y
wy,V,Rd y,c,Rd
M0
4
AW f
tM M
Combined Bending and Axial Resistance
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g
ForClass 1and Class 2cross-sections:
MEd MN,Rd whereMN,Rd is defined for a several different cross-sectionswithout fastener holes.
For Class 3 cross-sections the maximum longitudinal stress induced
(allowing for fasteners holes) by the combined actions must satisfy:
. A conservative alternative may be used for Class 1, Class 2
and Class 3 cross-sections as follows:
This provides a rapid, approximate solution.
y
x,Ed
M0
f
y,Ed z,EdEd
Rd y,Rd z,Rd
1,0M MNN M M
Combined Bending and Axial Resistance
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For Class 4 cross-sections the same limit for longitudinal stress applies
using the effective section properties where appropriate
A conservative alternative to the above criterion may be used as follows:
yx,Ed
M0
f
y,Ed Ed Ny z,Ed Ed NzEd
eff y M0 eff,y,min y M0 eff,z,min y M0
1,0M N e M N eN
A f W f W f
Combined Bending, Shear and Axial Resistance
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(1) Where shear and axial force are present, allowance should be made for the
effect of both shear force and axial force on the resistance moment.
(2) Provided that the design value of the shear force VEddoes not exceed 50% of
the design plastic shear resistanceVpl.Rdno reduction of the resistances defined
for bending and axial force in 6.2.9 need be made, except where shear buckling
reduces the section resistance, see EN 1993-1-5.
(3) WhereVEdexceeds 50% ofVpl.Rdthe design resistance of the cross-section to
combinations of moment and axial force should be calculated using a reduced
yield strength (1 )fyfor the shear area where = (2VEd/Vpl.Rd 1)2 andVpl,Rd
is obtained from 6.2.6(2).
Note:Instead of reducing the yield strength the plate thickness of the relevant part
of the cross-section may be reduced.
Buckling Resistance
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Types of buckling:
Dr. W.M.C. McKenzie84
Local buckling Flexural buckling
Plate buckling
Shear buckling
Distorsional buckling
P
P
Torsional buckling Torsional -flexural buckling
Snap buckling
Figure 21
Lateraltorsional buckling
Buckling ResistanceLocal Buckling
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Section Classification:
Dr. W.M.C. McKenzie85
Rotation
Class 2
Mp
Me
MM
oment
Class 1
Class 3
Class 4
Sections which have full plastic moment
and hinge rotation capacity.
Sections which have full plastic
moment capacity but not sufficient hinge
rotation capacity.
where:
Mp= plastic moment of resistance
Me= limiting elastic moment of resistance
M = elastic moment of resistance
Local buckling prevents development of
the plastic moment capacity.
Local buckling prevents the development of the yield
stress in one or more elements of the cross-section.
Figure 22
fy
fy
fy
fy
fy
fy
< fy
< fy
Class 1 Class 2 Class 3 Class 4
Buckling ResistanceLocal Buckling (cont.)
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Section Classification:
Dr. W.M.C. McKenzie86
Figure 23
Note:
c is the flat
portion of the
plate and the
base stressfy = 235 MPa
Buckling ResistanceClass 4 sections
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Effective section properties: effective widthbeffof planar elements
Dr. W.M.C. McKenzie87
beff= ( b)where, the reduction factor, is dependent on
the plate non-dimensional plate slenderness
Effective cross-sections for members
in compression
Figure 24
y
p
cr
wheref
p
Buckling ResistanceSlender sections in Compression
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Effective section properties:
Dr. W.M.C. McKenzie88
In doubly-symmetric sections the position
of the neutral axis does not change and
hence:
Nb,Rd=( Aefffy)/M1In singly-symmetric cross-sections, or
asymmetric cross-sections the formation of
effective holes may lead to a shift in the
position of the neutral axis,eN.
The compressive load (NEd), is then eccentric
to the effective cross-section neutral axis and
will cause a secondary bending moment:
M = (NEd eN)The section should be checked for a
combined stress conditionFigure 25
Buckling ResistanceSlender sections in Bendingi i
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EN 1993-1-5:
Table 4.1:
Internal elements
Table 4.1:
Internal elementsTable 4.2:
Outstand elements
Table 4.2:
Outstand elements
Note:the change in the position
of the neutral axis in each case.
Effective section properties:
Figure 26
compression zone
e
Buckling ResistanceSlender sections in Bendingi i
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Effective section properties:EN 1993 -1- 5: 2006
Section 4.4
Effective areas for slendercross-sections
Figure 27Figure 28
1st. term is the von Karman contribution forbuckling of an ideally perfect plate.
2nd. term is to allow for out-of-plane imperfections,
residual stresses and interaction between yielding
and plate buckling.
Internal compression elements
Buckling ResistanceEffective section
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b
hf
hw
tw
1
2
Non-effective zones
-ve - tension
+ve - compression
hf
Figure 29
Verification for Buckling Resistance
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Verification is carried out where appropriate for sections at the ultimate
limit state in relation to:
flexural buckling, (NEd /Nb,Rd 1,0) Clause 6.3.1 lateral torsional buckling, (MEd /Mb,Rd 1,0)Clause 6.3.2 combined bending and axial compression, Clause 6.3.3
y,Ed y,Ed z,Ed z,EdEdyy yz
y Rk y,Rk z,Rk
LT
M1M1 M1
y,Ed y,Ed z,Ed z,EdEdzy zz
z Rk y,Rk z,R k
LTM1 M1M1
1 0
1 0
M M M MNk k ,
N M M
M M M MN k k ,N M M
Buckling ResistanceFlexural Buckling
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Nb,Rdis taken as the smaller of:
(a) for Class 1, Class 2 or Class 3 cross-sections.
or
(b) for Class 4 cross-sections.
whereAeff is the effective cross-sectional area determined in accordancewith EN 1993-1-5 and is a reduction factor for flexural, torsional orflexural torsional buckling.
yb,Rd
M1
AfN
eff y
u,Rd
M1
A fN
Buckling ResistanceFlexural Buckling
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Reduction Factor:
where for Class 1, 2 and 3 cross-sections,
for Class 4 cross-sections,
and is the non-dimensional slenderness.
is an imperfection factor which depends on the shape of the column cross-section, the axis of buckling the fabrication process and the steel grade.
The value of can also be obtained from buckling curves given in the code.
2
2 2
1 but 1,0 where = 0,5 1+ 0,2
y
cr
Af
eff y
cr
A f
2
cr 2cr
EI
L
Not given in EC3
Buckling ResistanceFlexural Buckling
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Typical Stress/Slenderness Curve
EC3 - Euler slenderness 1 = (E/fy)0,5 = 93,9(assuming E= 210 103 MPa and fy = 235 MPa)
Slenderness
fy
Failure by
bucklingFailure by
yielding
Euler buckling
curve
P
1
Plastic buckling
Local and flexural buckling
Figure 30
Buckling ResistanceFlexural Buckling
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Figure 31
EC3Non-dimensional buckling curve
Safe lower-bound
design curve in EC3
non-dimensional slenderness = ( /1)
1,0
= /fyP
1,0
* *
*
*
*
*
*
*
*
** *
*
*
*
*
*
* *
**
*
***
*
*
*
**
Failure predicted by Euler
Actual test results
0,2
Typical Stress/Non-dimensional Slenderness Curve
Buckling ResistanceCritical Buckling Length
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The only advice given in EC 3
regarding the buckling lengths of
members is in the informative
Annex BB.
In the absence of further information it
is likely that UK engineers will adopt
the effective length values given in
BS 5950: Part 1
Figure 32
Buckling ResistanceBS5950 Buckling Lengths
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Figure 33
T pical Red ction Factor/Non dimensional Slenderness C r e
Buckling ResistanceBuckling Curves
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Figure 34
Typical Reduction Factor/Non-dimensional Slenderness Curve
For non-dimensional slenderness values 0,2 orNEd/Ncr 0,04 buckling
effects may be ignored and only cross-section checks are required.
Tables given in BS 5950 representing the buckling curves
Buckling ResistanceBuckling Curves
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Figure 35
Tables given in BS 5950 representing the buckling curves
Buckling ResistanceTorsional and Torsional-flexural Buckling
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Figure 36
Torsional and torsional-flexural
buckling is generally significant in
cold-formed sections since they are
fabricated from relatively thin
material and are of open section.
Ncr = Ncr,TF but < Ncr,T.
The relevant buckling curve is the
one associated with thez-zaxis.
Single open sections
Open built-up sections
Closed built-up sections
Typical forms of sections for cold-formed members
Buckling ResistanceLateral Torsional Buckling
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MbRdis taken as the smaller of:
(a) for Class 1, Class 2 cross-sections.
(b) for Class 3 cross-sections.
(c) for Class 4 cross-sections.
whereLTis the reduction factor for lateral torsional buckling and theWyisthe appropriate plastic, elastic or effective section modulus.
yb,Rd LT pl,y
M1
fM W
y
b,Rd LT el,y
M1
fM W
y
b,Rd LT eff,y
M1
fM W
fy
fy
fy
fy
< fy
< fy
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Reduction Factor:LT1. General case:
The general case may be applied to all common section types including
rolled sections, plate girders, castellated and cellular beams. The buckling
curves given in Figure 6.4 of EC 3 can be used with to determineLToralternatively Equation (6.56) may be used.
2. Rolled sections or equivalent welded sections (i.e. same size?)In this case the value ofLTis determined using Equation (6.57) and may bemodified to take into account the moment distribution between the lateral
restraints.
LT
Buckling ResistanceLateral Torsional Buckling
No need to check lateral torsional buckling
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The general case is less favourable than the one for rolled and equivalent
sections and the plateau is longer potentially offering significant savings.
1,0
0,8
0,6
0,4
0,2
2,01,51,00,50
Rolled and equivalent
welded sections
(Clause 6.3.2.3)
General case
(Clause 6.3.2.2)Red
uctionfactor-LT
Slenderness -LT
No need to check lateral torsional buckling
for below the values indicated.
(Note: curves shown are indicative only)
Figure 37
Reduction Factor LT
Buckling ResistanceLTB: General Case
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Reduction Factor LT
where:
Mcr is the elastic critical moment for elastic bucklingFormulation is not given in EC3
LTis an imperfection factor given in Table 6.3 of EN 1993-1-1
The evaluation ofMcr is considered textbook material and there is a lack of
consensus on the true value. EN 1993 merely states that Mcr is based on the gross
cross-sectional area and takes into account the loading, the real moment
distribution and the lateral restraints.
Dr. W.M.C. McKenzie105
LT LT2 2
LT LT LT
1 but 1,0
2LT LT LT LT= 0,5 1+ 0,2
y yLT
cr
W f
M
El ti iti l t M
Buckling ResistanceLTB: General Case
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Elastic critical momentMcr
The elastic critical moment Mcr at which lateral torsional buckling is induced is
dependent on a number of variables one of which is the critical buckling length Lcr.
No guidance is given in EC3 regarding calculatingLcr. or the requirements for the
lateral restraints (?) refer to BS 5950.
It is generally assumed that the standard conditions of restraint at the end of a beam
are:
restraint against lateral movement,
restraint against rotation about the longitudinal axis and
the beam is free to rotate in plan.
Dr. W.M.C. McKenzie106
Buckling ResistanceLTB: General Case
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107
Figure 38L cr
L cr
L cr
Intermittent restraint provided
by secondary beams
Note:In Clauses 4.3.2 and 4.3.3 of BS 5950: Part 1 it is required that intermediate lateral
restraints are required to be capable of resisting a total force of not less than 2,5% of
the maximum design axial force in the compression flange within the relevant span,
divided between the intermediate lateral restraints in proportion to their spacing.
Buckling ResistanceLTB: Elastic Critical Moment
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Evaluation ofMcr
The elastic critical moment for LTB of a beam of uniform symmetricalcross-section with equal flanges, under standard conditions of restraint at
the ends, loaded through the shear centre and subject to a uniform moment
throughout is given by:
0,5
22w crz
cr 2 2zcr z
where2 1
TI L GI EI E
M GIL EI
M M
LM MFundamental case
= 1,0
Figure 39
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Elastic critical moment for lateral torsional buckling factor -C1
= +1,0 C1 = 1,000
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110
= 0,75 C1 = 2,57
= 1,0 C1 = 2,55
= +0,75 C1 = 1,14
= +0,50 C1 = 1,31
= +0,25 C1 = 1,52
= 0 C1 = 1,77
= 0,50 C1 = 2,33
= 0,25 C1 = 2,05
UDL pinned supports
C1 = 1,046
C1 = 1,127
C1 = 2.578
C1 = 1,348
C1 = 1,683
UDL fixed supports
Central point load
pinned supports
Central point load
fixed supports
span point loadsFigure 40
Buckling ResistanceLTB: Elastic Critical Moment
Th l l i h d l d di i b i d
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111
The values relating to the end moment load conditioncan be estimated
using the following equation*:
C1 1,881,4 + 0,522 2,70
*
Galambos, T.V. (ed.) (1998)
Guide to Stability Design Criteria for Metal Structures,
5th. edn. Wiley, New York.
Figure 41-1,0 -0,75 -0,50 -0,25 0,0 0,75 1,00,25 0,50
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
Ratio of end moments -
C1
more exact solution
approximate solution
cut-off value
Buckling ResistanceLTB: Elastic Critical Moment
Th l l i d bl i i b b i d f h
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112
The values relating to doubly symmetric sections can be obtained from the
NCCI: SN003a-EN-EU. This NCCI gives the expression of the elastic
critical moment for doubly symmetric cross-sections. Values of the factors
involved in the calculation are given for common cases. For a beam under
a uniformly distributed load with end moments or a concentrated load at
mid-span with end moments, the values for the factors are given in graphs.
L is the length between points which have lateral restraintkis an effective length factors referring to end rotation about z-z
kw are effective length factors referring to end warping
zg is the distance between the point of load application and the shear centre.
Note :for doubly symmetric sections, the shear centre coincides with the centroid.
2 22
2crwzcr 1 2 22 2
z zcr
T
g g
w
kL GI IEI kM C C z C z
k I EIkL
Figure 42
Buckling ResistanceLTB: Elastic Critical Moment
NCCI: SN003a EN EU (see http://www access steel com/)
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113
NCCI: SN003a-EN-EU. (see http://www.access-steel.com/)
Figure 43
Graphs to determine C1 and C2 values for UDLs and mid-span point
loads combined with end moments.
Buckling ResistanceLTB: Elastic Critical MomentThe value ofMcrcan also be calculated using theLTBeamsoftware which
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can be downloaded from http://www.cticm.com FREE
Figure 44
Buckling ResistanceLTB: Rolled Sections andEquivalent Welded Sections
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Reduction Factor LT
where: and as before.
In the UK National Annex:
= 0,4 for rolled sections and 0,2 for equivalent welded sections,
= 0,75 for rolled sections and 1,0 for equivalent welded sections
The imperfection factor LTis obtained from Table 6.3. The Table 6.4 values for
selection of the appropriate buckling curve have been modified in the UK N.A.
Dr. W.M.C. McKenzie115
Equivalent Welded Sections
LT 2 2LT LT LT
2LT
1
1,0
1
2LT LT LT LT,0 LT= 0,5 1+ y y
LTcr
W f
M
LT,0
Do not use the buckling curves given in
Figure 6.4 of the code, i.e calculate LT.
Buckling ResistanceLTB: Rolled Sections andEquivalent Welded Sections
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The selection of the appropriate buckling curve: EN 1993-1-1
Dr. W.M.C. McKenzie116
Equivalent Welded Sections
The selection of the appropriate buckling curve: UK N.A. to EN 1993-1-1
Figure 45
Buckling ResistanceLTB: Rolled Sections andEquivalent Welded Sections
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The modification factorfto be applied to LT:The reduction factor may be modified to take into account the shape of the
bending moment diagram between the restraints, i.e.
f= 1 0,5(1 kc)[1 2,0( 0,8)2] 1,0 wherekcis given in Table 6.6
In the UK Annex
From UK N.A.
Dr. W.M.C. McKenzie117
LTLT,mod 1,0
f
LT
c1
1k
C
Figure 46
Buckling ResistanceCombined Bending andAxial Compression
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pInteraction Equations:
The My,Edand Mz,Edterms allow for the additional moment which occurs due to
the shift in the neutral axis when using effectivecross-sectional area for Class 4
cross-sections.
Values for the interaction factorski,jfor the formulae can be determined as indicated
in Annex A orAnnex B.they are very complex and time consuming to evaluate.
y,Ed y,Ed z,Ed z,EdEd
yy yzy Rk y,Rk z,Rk
LT
M1M1 M1
y,Ed y,Ed z,Ed z,EdEdzy zz
z Rk y,Rk z,R k
LTM1 M1M1
1 0 Equation (6.61)
1 0 Equation (6.62)
M M M MN
k k ,N M M
M M M MNk k ,
N M M
Buckling ResistanceCombined Bending andAxial CompressionAnnex A:
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Figure 47
Buckling ResistanceCombined Bending andAxial CompressionAnnex B:
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Figure 48
Buckling ResistanceCombined Bending andAxial Compression
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UK NA to EN 1993-1-1:
Figure 49
Buckling Resistance Combined Bending andAxial Compression for Columns in SimpleC t ti
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122
Construction
NCCI: SN048b-EN-GB
Figure 50
Buckling Resistance Combined Bending and AxialCompression for Columns in Simple Construction
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123
NCCI: SN048b-EN-GB
Figure 51
Buckling Resistance Combined Bending and AxialCompression for Columns in Simple Construction
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124
NCCI: SN048b-EN-GB
Figure 52
Serviceability Limit States: Verification for Deflection
For characteristic combinations: EN 1990:2002
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125
EN 1993-1-1 indicates that serviceability limit states, i.e. deflection,
vibration etc., and their associated loading/analysis models should be
agreed with the client and specified for a project. Reference shouldbe made to the National Annex for any appropriate limits.
In the UK N.A. information is given relating to:
vertical deflections, horizontal deflections and
dynamic effects.
k,j k,1 0,i k,i
1 1
Equation (6.14b)p
j i
G P Q Q
Serviceability Limit States: Verification for Deflection
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126
Figure 53
Use only the
variable loads
Maintenance of the Eurocodes
CEN is responsible for maintenance of the Eurocodes and has
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p
developed an appropriate strategy for revision and updating.
Maintenance activities deal with:
processing comments from the users,
correction of errors,
technical amendments,
editorial improvements,
resolution of questions of interpretation,
elimination of inconsistencies and misleading statements.
Dr. W.M.C. McKenzie
127
Use of the Eurocodes Outside the EU
Several countries already use the Eurocodes for the revision of
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Several countries already use the Eurocodes for the revision of
existing codes and the creation of new ones.
Several countries are planning the direct implementation of the
Eurocodes.
A number of structural engineers in companies that participatein international projects are using the Eurocodes.
There are Universities outside Europe who are offering courses
on Eurocodes.
Dr. W.M.C. McKenzie
128
Do not underestimate the amount of investment in time and effort required,
particularly if dealing with several materials!
Education/TrainingCPD Provision:
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Professional bodies, e.g. (tonight)
ICE, I.Struct.E., SCI, Concrete Centre, TRADA, BDA
Universities, Colleges etc. e.g. recent Edinburgh Napier short courses
Web Resources, e.g.
http://eurocodes.jrc.ec.europa.eu
http://www.cticm.com
http://www.access-steel.com/
Textbook Publications & Software e.g. Thomas Telford Design Guides and
The Behaviour and Design of Steel Structures to EC3 by N S Trahair et al.
ISBN 978-0-415-41866-9,LTbeamsoftware etc.
Dr. W.M.C. McKenzie
129
The Future
Exciting and
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BS 449, BS 5950
Slide Rule
Eurocodes!!!!
Note Book!!
Exciting and
challenging
opportunities for
innovation using
the worlds mostadvanced design
codes and
sophisticatedsoftware analyses.Th k Y
top related